7.8. Layered liquids on an inclined surface Simultaneous flow of two or more thin layers of liquid is needed to form various composite coatings. Suppose that immiscible liquids 1 and 2 flow down a surface that is inclined at an angle relative to vertical, as shown in Fig. P7.8. The respective layer thicknesses are H1 and H2, the densities are 1 and 2, the viscosities are 1 and 2, and the fully developed velocities are vx(1)(y) and vx(2)(y). As usual, it may be assumed that the air pressure is constant at P0 and that viscous stresses in the air are negligible. Figure P7.8 Flow of immiscible liquids down an inclined surface. (a) What is dP/dx in liquid 1 ? (b) What is dP/dx in liquid 2? (c) State the differential equations and boundary conditions and find vx(1)(y) and vx(2)(y). 7.8. Layered liquids on an inclined surface Simultaneous flow of two or more thin layers of liquid is needed to form various composite coatings. Suppose that immiscible liquids 1 and 2 flow down a surface that is inclined at an angle relative to vertical, as shown in Fig. P7.8. The respective layer thicknesses are H1 and H2, the densities are 1 and 2, the viscosities are 1 and 2, and the fully developed velocities are vx(1)(y) and vx(2)(y). As usual, it may be assumed that the air pressure is constant at P0 and that viscous stresses in the air are negligible. Figure P7.8 Flow of immiscible liquids down an inclined surface. (a) What is dP/dx in liquid 1 ? (b) What is dP/dx in liquid 2? (c) State the differential equations and boundary conditions and find vx(1)(y) and vx(2)(y)